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Introduction to Research Methods in Political Science:
The POWERMUTT* Project
(for use with SPSS)

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Resources for introductory research methods courses in political science and related disciplines

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IV. DISPLAYING CATEGORICAL DATA  

Subtopics

SPSS Tools

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Introduction

A picture is said to be worth a thousand words.  Tables and graphs, properly designed, can provide clear pictures of patterns contained in many thousands of pieces of information.   In this topic, we will describe several ways of displaying information about categorical variables in tabular and graphic form.  In later topics, ways of displaying information about continuous variables will be explained.


Frequency Tables

A frequency table (or frequency distribution) displays numbers and percentages for each value of a variable.  It is useful for categorical variables (that is, those with values falling into a relatively small number of discrete categories, such as party identification, religious affiliation, or region of a country) rather than for continuous variables (such as age in years or gross domestic product in dollars). 

The following frequency distribution shows, by region of the country, how many state legislatures are controlled by each major party. (In four states, each party controls one of the state's two houses, while in one state, Nebraska, the legislature is officially non-partisan.

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Party Control of State Legislatures

The first column in the table provides a label for each category of the variable.  The second and third columns show, respectively, the number and percent of cases in each category for all cases.   The fourth column shows the percent in each category after eliminating cases for which we do not have information (missing data).  Since we know the party composition of every state legislature, the fourth column is identical to the third in this case.   The last column shows the cumulative percentages as one goes from the first to the last category.  Note that this last column makes sense only if the values of the variable can be meaningfully ranked.  In other words, cumulative frequencies assume at least ordinal level measurement.  The numbers in this column make no sense in this example, since it wouldn't be meaningful to say that "98 percent of state legislatures have split majorities or less.


Contingency Tables

A contingency table (also called a crosstabulation, or crosstab for short) displays the relationship between one categorical variable and another.  It is called a “contingency table” because it allows us to examine a hypothesis that the values of one variable are contingent (dependent) upon those of another.

The following crosstabulation shows the relationship between control of state legislatures and region of the country at the start of the 113th Congress (2013-2014):

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Party Control of State Legislatures by Region

There are several important things to notice about the way in which the table has been set up:

Do not let all the trees get in the way of seeing the forest.  In interpreting a crosstab, it is crucial to focus on the overall picture.  In this case, the table shows that there are substantial regional differences in party strength.  Don’t get bogged down in the details. 


Making Tables Presentable

The frequency distributions and crosstabs are presented above just as they were generated by SPSS.  This is the way in which tables will normally be presented in POWERMUTT, so that you can run your own analyses and compare your results to what is presented here.  For use in a term paper, however, you will probably want tables that are more aesthetic.  The following tables are a little more presentable, and also contain a bit more information, including 1) a title that briefly describes what the table is about, and 2) the source of the data (as referenced in the codebook) used to generate the table.  By the same token, a lot of extraneous information has been omitted.  Tables usually present information only for valid cases.  Cumulative percentages are omitted from Table 1, since region is only a nominal variable.  Individual cell counts and row totals are omitted from Table 2, since this information can be reconstructed if needed from the information that is provided.  Ask your instructor whether it will be sufficient to copy and paste tables from SPSS into your word processor or whether you will need more formal tables such as shown here.

Table 1:
Party Control of State Legislatures, 2013

 
# of States
Percent
Party Control
Democrat
19
38
Republican
26
52
Split
4
4
Non-partisan
 1
 2
  Totals
50
100
 
Source: National Conference of State Legislatures, "2012 Live Election Night Coverage of State Legislative Races," http://www.ncsl.org. Accessed November 10, 2012.

Table 2:
Party Control of State Legislatures by Region, 2013

 
Northeast
Midwest
South
West
Party Control
   
Democrat
  77.8%
  16.7%
  18.8%
  53.8%
Republican
 11.1
 66.7
 68.8
 46.2
Split
 11.1
  8.3
 12.5
  0.0
Non-partisan
  0.0
  8.3
  0.0
  0.0
  Totals
100.0
100.0
100.0
100.0
  N
9
12
16
13
 
Source: National Conference of State Legislatures, "2012 Live Election Night Coverage of State Legislative Races," http://www.ncsl.org. Accessed November 10, 2012.

 

 

 

 

 

 

 

 


Pie Charts

A pie chart is a simple way to show the distribution of a variable that has a relatively small number of values, or categories.  Figure 1 provides in graphic form information similar to what table 1 (above) presents in tabular form:

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Figure 1:
Piechart showing party control of state legislatures

Similarly figure 2 is analogous to table 2, and breaks the results down by region:

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Figure 2:
Piechart showing party control of state legislatures by region

Bar Charts

Another way to portray the information contained in table 1 and figure 1 is with a bar chart, as shown in figure 3:  

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Figure 3:
Barchart showing party control of state legislatures

Finally, figure 4 shows a "clustered" bar chart, with results displayed for each region. It is similar to table 2 and figure 2.

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Figure 4:
Barchart showing party control of state legislatures by region


Key Concepts

bar chart
contingency table
crosstab
crosstabulation
frequency distribution
frequency table
pie chart


Exercises

These exercises use the 2008 American National Election Study Subset. Open the codebook describing these data. Start SPSS and open the anes08s.sav file.

1.  Prepare a frequency table, pie chart, and bar chart for an economic, social, or foreign policy issue of your choosing (see codebook).  Crosstabulate this with several background variables (again, see codebook) that you think might influence a respondent's opinion on this issue. Cautions: 1) avoid background variables like age or income that have a large number of categories; 2) some categories of some background variables contain very few cases, and the results are likely to be unreliable. In another topic, we'll discuss how measures of statistical significance can help you better assess the reliability of findings. In yet another topic, we'll also show you how to modify variables to make them more manageable.

Convert your frequency and contingency tables into presentation-ready form.   

2.  In exercise 1 of the “Political Science as a Social Science” topic, you were asked to come up with hypotheses that might help explain party identification. Using "partyid3" as the dependent variable, construct contingency tables to test the following hypotheses, along with any others you can think of:

  • Men are more likely than women to identify as Republicans, while women are more likely than men to identify as Democrats.
  • Southerners and midwesterners are more likely than others to identify as Republicans; northeasterners and westerners are more likely than others to identify as Democrats.
  • Respondents from union households are more likely than those from nonunion households to identify as Democrats.
  • Married respondents are more likely than others to identify as Republicans.
  • The more regularly people attend religious services, the more likely they are to identify as Republicans.
  • Whites are less likely than others to identify as Democrats.
Were the results of these exercises pretty much what you expected, or were there any surprises?

For Further Study

Energy Information Administration, “Energy Explained: Your Guide to Understanding Energy,” Official Energy Statistics From the Government. I http://www.eia.doe.gov/pub/oil_gas/petroleum/analysis_publications/oil_market_basics/graphs_and_charts.htm.

Gostats.com, "Graphing and Types of Graphs," GoStats. http://gostats.com/resources/types-of-graphs.html.

Math League Multimedia, “Using Data and Statistics,” The Math League. http://www.mathleague.com/index.php?option=com_content&view=article&id=69.

Social Science Research and Instructional Council, "Links to Other Instructional Sites: Graphs," http://www.ssric.org/tr/links#graphs.


[1] On occasion, crosstabs are used, not to test hypotheses, but for descriptive purposes, and this general rule does not apply. For example, the 2008 American National Election Study Subset (see codebook) includes several variables thought to measure political efficacy (a person's belief that he or she can have an impact on politics). If these variables are valid measures of the same underlying concept, there should be a relationship between answers to one question and those to another, but we are not hypothesizing that either one depends on the other. In trying to see whether this is the case, we may decide to look, for each cell in the table, at the percent of the total table rather than of either the row or column.

[2] A more systematic method for assessing the reliability of percentages in a crosstab is discussed under the topic of contingency table analysis.

 


Last updated April 28, 2013 .
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